A new method for calculating the velocity ellipsoid

Abstract

The velocity ellipsoid has traditionally been calculated by use of moments of the velocity components after the distribution of parallaxes has been corrected for parallax error. An alternative, used in this study, fits a quadric surface to the velocity components and reduces the data by use of a new mathematical technique, semidefinite programming, and a criterion, difference of squares, that calculates a unique ellipsoid that represents a global minimum of the reduction criterion. Use is made of 246 stars of spectral class O-B5 and luminosity class V to calculate the velocity ellipsoid. The results may be considered superior to those found from the method of moments.